It may be observed of mathematicians that they only meddle with such things as are certain, passing by those that are doubtful and unknown. They profess not to know all things, neither do they affect to speak of all things. What they know to be true, and can make good by invincible arguments, that they publish and insert among their theorems. Of other things they are silent and pass no judgment at all, chusing [choosing] rather to acknowledge their ignorance, than affirm anything rashly. They affirm nothing among their arguments or assertions which is not most manifestly known and examined with utmost rigour, rejecting all probable conjectures and little witticisms. They submit nothing to authority, indulge no affection, detest subterfuges of words, and declare their sentiments, as in a Court of Judicature [Justice], without passion, without apology; knowing that their reasons, as Seneca testifies of them, are not brought to persuade, but to compel.

My fathers collection of fossils was practically unnamed, but the appearance of Phillips book [Geology of the Yorkshire Coast], in which most of our specimens were figured, enabled us to remedy this defect. Every evening was devoted by us to accomplishing the work. This was my first introduction to true scientific study. ... Phillips accurate volume initiated an entirely new order of things. Many a time did I mourn over the publication of this book, and the consequences immediately resulting from it. Instead of indulging in the games and idleness to which most lads are prone, my evenings throughout a long winter were devoted to the detested labour of naming these miserable stones. Such is the short-sightedness of boyhood. Pursuing this uncongenial work gave me in my thirteenth year a thorough practical familiarity with the palaeontological treasures of Eastern Yorkshire. This early acquisition happily moulded the entire course of my future life.

Science and art are only too often a superior kind of dope, possessing this advantage over booze and morphia: that they can be indulged in with a good conscience and with the conviction that, in the process of indulging, one is leading the higher life.

The science of calculation is indispensable as far as the extraction of the square and cube roots: Algebra as far as the quadratic equation and the use of logarithms are often of value in ordinary cases: but all beyond these is but a luxury; a delicious luxury indeed; but not to be indulged in by one who is to have a profession to follow for his subsistence.

What [man landing on the moon] is doing up there is indulging his obsession with the impossible. The impossible infuriates and tantalizes him. Show him an impossible job and he will reduce it to a possibility so trite that eventually it bores him.

In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion.
(1987) -- Carl Sagan